Optimal. Leaf size=70 \[ -\frac {1}{8 x^8}-\frac {11}{7 x^7}-\frac {55}{6 x^6}-\frac {33}{x^5}-\frac {165}{2 x^4}+\frac {x^3}{3}-\frac {154}{x^3}+\frac {11 x^2}{2}-\frac {231}{x^2}+55 x-\frac {330}{x}+165 \log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 70, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {27, 43} \begin {gather*} \frac {x^3}{3}+\frac {11 x^2}{2}-\frac {231}{x^2}-\frac {154}{x^3}-\frac {165}{2 x^4}-\frac {33}{x^5}-\frac {55}{6 x^6}-\frac {11}{7 x^7}-\frac {1}{8 x^8}+55 x-\frac {330}{x}+165 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin {align*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^9} \, dx &=\int \frac {(1+x)^{11}}{x^9} \, dx\\ &=\int \left (55+\frac {1}{x^9}+\frac {11}{x^8}+\frac {55}{x^7}+\frac {165}{x^6}+\frac {330}{x^5}+\frac {462}{x^4}+\frac {462}{x^3}+\frac {330}{x^2}+\frac {165}{x}+11 x+x^2\right ) \, dx\\ &=-\frac {1}{8 x^8}-\frac {11}{7 x^7}-\frac {55}{6 x^6}-\frac {33}{x^5}-\frac {165}{2 x^4}-\frac {154}{x^3}-\frac {231}{x^2}-\frac {330}{x}+55 x+\frac {11 x^2}{2}+\frac {x^3}{3}+165 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 70, normalized size = 1.00 \begin {gather*} -\frac {1}{8 x^8}-\frac {11}{7 x^7}-\frac {55}{6 x^6}-\frac {33}{x^5}-\frac {165}{2 x^4}+\frac {x^3}{3}-\frac {154}{x^3}+\frac {11 x^2}{2}-\frac {231}{x^2}+55 x-\frac {330}{x}+165 \log (x) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^9} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 62, normalized size = 0.89 \begin {gather*} \frac {56 \, x^{11} + 924 \, x^{10} + 9240 \, x^{9} + 27720 \, x^{8} \log \relax (x) - 55440 \, x^{7} - 38808 \, x^{6} - 25872 \, x^{5} - 13860 \, x^{4} - 5544 \, x^{3} - 1540 \, x^{2} - 264 \, x - 21}{168 \, x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 59, normalized size = 0.84 \begin {gather*} \frac {1}{3} \, x^{3} + \frac {11}{2} \, x^{2} + 55 \, x - \frac {55440 \, x^{7} + 38808 \, x^{6} + 25872 \, x^{5} + 13860 \, x^{4} + 5544 \, x^{3} + 1540 \, x^{2} + 264 \, x + 21}{168 \, x^{8}} + 165 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 59, normalized size = 0.84 \begin {gather*} \frac {x^{3}}{3}+\frac {11 x^{2}}{2}+55 x +165 \ln \relax (x )-\frac {330}{x}-\frac {231}{x^{2}}-\frac {154}{x^{3}}-\frac {165}{2 x^{4}}-\frac {33}{x^{5}}-\frac {55}{6 x^{6}}-\frac {11}{7 x^{7}}-\frac {1}{8 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 58, normalized size = 0.83 \begin {gather*} \frac {1}{3} \, x^{3} + \frac {11}{2} \, x^{2} + 55 \, x - \frac {55440 \, x^{7} + 38808 \, x^{6} + 25872 \, x^{5} + 13860 \, x^{4} + 5544 \, x^{3} + 1540 \, x^{2} + 264 \, x + 21}{168 \, x^{8}} + 165 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 58, normalized size = 0.83 \begin {gather*} 55\,x+165\,\ln \relax (x)-\frac {330\,x^7+231\,x^6+154\,x^5+\frac {165\,x^4}{2}+33\,x^3+\frac {55\,x^2}{6}+\frac {11\,x}{7}+\frac {1}{8}}{x^8}+\frac {11\,x^2}{2}+\frac {x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 61, normalized size = 0.87 \begin {gather*} \frac {x^{3}}{3} + \frac {11 x^{2}}{2} + 55 x + 165 \log {\relax (x )} + \frac {- 55440 x^{7} - 38808 x^{6} - 25872 x^{5} - 13860 x^{4} - 5544 x^{3} - 1540 x^{2} - 264 x - 21}{168 x^{8}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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